The Dynamics of Continued Fractions

I love working on conjectures. Just as in the various Mathematical Olympi- ads in which I have participated, the conditions are already set; the challenge consists in cleverly using the hypotheses of the problem to produce the conjectured conclusion. Number theory, the study of properties of the ordinary counting numbers 1; 2; 3; : : :, is particularly rich in this type of problems, which range from puzzles for the general audience to the challenges on the Interna- tional Mathematical Olympiad to famous conjectures, such as Fermat’s Last Theorem and the Twin Prime Conjecture, which commonly remain unsolved for hundreds of years. My instincts told me that Conrad’s problem would not be one of these enduring conjectures, and eagerly I set to work.

• Mathematics